Question

What type of triangle is shown in the figure?

a). Obtuse
b). Right Angled
c). Isosceles
d). Acute

Answer 1

Hint: We see that we are given the measure of the angles in the triangle. Also, all the angles are less than \[{90^ \circ }\]. An angle is called a right angle if its measure is equal to \[{90^ \circ }\]. Obtuse angle is the angle whose measure is more than \[{90^ \circ }\]and less than \[{180^ \circ }\]And acute angle is the angle whose measure is more than \[{0^ \circ }\]and less than \[{90^ \circ }\]. In this question, we have to identify the type of triangle in the figure where measure of angles of the triangle is given. For that, we will first understand the definition of the types of triangles given in options and then we will make a decision for the final answer.

Complete step-by-step solution:
We first see the definition of All the four types of triangles given in the options.
a). OBTUSE TRIANGLE – A triangle in which the measure of any one angle is more than \[{90^ \circ }\]and the measure of the remaining two is less than \[{90^ \circ }\]is called an obtuse triangle. i.e. A triangle with one obtuse angle and two acute angles is called an obtuse triangle.
b). RIGHT ANGLED TRIANGLE – A triangle in which the measure of any one angle is equal to \[{90^ \circ }\]and the measure of other two is less than \[{90^ \circ }\]is called right angled triangle. i.e. A triangle with one right angle and other two acute angles is called Right angled triangle.
c). ISOSCELES TRIANGLE – A triangle in which the length of any two sides are equal or we can say that a triangle in which the measure of any two angles is the same and the third angle can be of any measure.
d). ACUTE – A triangle in which the measure of all angles of the triangle is less than \[{90^ \circ }\]is called acute triangle. i.e. A triangle in which all the angles are acute, is called Acute triangle.
In the given figure, we see that the measure of all the angles is less than \[{90^ \circ }\]and no two angles are equal.
So, from the above definitions, we see that the Triangle in the given figure is Acute Triangle.
\[\therefore \]The correct option is (d).

Note: We need to see the figure very carefully and then we should be very clear with the angles’ name. If we interchange the conditions for angles ,we will reach the wrong answer. All the definitions of the type of triangles are to be read very carefully because there is a minor difference in the conditions. In this question, we should be very careful that we just don’t have to see that all angles are less than \[{90^ \circ }\]so it is acute. We need to check if any of the two angles are equal or not as even if all the angles are acute but two of them are equal then it will be an isosceles triangle.